Answer:
x = -0.2 and x = -3.5
Step-by-step explanation:
Combine like terms in the given equation, by subtracting 2x^2 from both sides:
6x^2 + 15x + 3 = 2x^2
-2x^2 = -2x^2
----------------------------------
4x^2 + 15x + 3 = 0
This is a quadratic equation. We'll find the two solutions using the quadratic equation
-b ± √(b^2 - 4ac)
x = ---------------------------
2a
Here the coefficients of the quadratic are a = 4, b = 15 and c = 3.
Thus, the discriminant b^2 - 4ac is 15^2 - 4(4)(3), or +177
and from that we know we'll find two real, unequal roots.
-15 ± √177
The roots are: x = ------------------- , or x = -0.2 and x = -3.5
8
Answer:
the home is
5.83 blocks 31° North of west of the school
Step-by-step explanation:
Resolving the displacement to vertical and horizontal axis
Let north and south represent positive and negative vertical axis, also east and west represent positive and negative horizontal axis;
Vertical axis; , 2 blocks south to visit her aunt, then 5 blocks north to go home
Ry = -2 + 5
Ry = +3
Horizontal axis; 5 blocks west to the grocery store
Rx = -5
Resultant distance = R = √(Rx^2 + Ry^2)
R =√(-5^2 + 3^2)
R = √34
R = 5.83 blocks
For the direction;
∅ = arctan(Ry/Rx) = arctan(3/5)
∅ = 31°
Therefore, the home is
5.83 blocks 31° North of west of the school.
Answer:
18 ounces of barley
Step-by-step explanation:
If Meg uses barley and wheat flour in a ratio of 2:3, we can set up equivalent ratios in order to find how many ounces of barley Meg would need if she uses 27 ounces of wheat flour:
= =
We can solve for 'x' (the number of ounces of barley) using a few different methods. We can cross-multiply and divide: 27(2) = 3x, or x = 18. We can also see what factor we multiply the 3 by to get 27 and multiply the numerator (2) by the same number. Since 3 x 9 = 27, then 2 x 9 = 18.
Answer: b)
Step-by-step explanation:
3^3 is equal to 27 exactly, but it asks for an approximate. 27.55 is near 27 so yea, there ya go ^